# Stochastic Optimization in Random Fitness Landscapes

Faculty Department of Project Supervisor:

Faculty of Engineering and Natural Sciences

Consider a set of nodes (e.g. genotypes in the biology setting) in a random network. Suppose that a set of ‘fitness’ (e.g. growth rate) measurements of each node under a set of external forces (e.g. antibiotics) are given. The transition probabilities of a ‘realization’ of a Markov chain (or a fitness landscape) associated with each arc under each external force are computable via a predefined function given the fitness value realizations of each pair of nodes. The aim is to maximize the probability of reaching to a particular node given the initial node in a predetermined number of transitions, considering the following two sources of uncertainties in this problem: i) the randomness in fitness observations, ii) the transition probabilities, which are functions of fitness observations. In this project, we will use a stochastic mixed-integer programming approach to solve this problem.

Prospective students must have strong background (at least B letter grade) in optimization (at least IE 311 level) and computing (at least CS 201 level).

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